Influence de la topographie sur les ondes de surface

Abstract : This work deals with the water waves problem for uneven bottoms in the long-wave framework. We aim here at constructing, justifying and comparing new asymptotic models taking into account the bottom topography. First, two new classes of symmetric Boussinesq-like models are rigorously derived for two different topographical regimes, one for small bathymetrical variations and one for strong variations. In a second part, we recover and discuss the classical Korteweg-de Vries approximation in the regime of small topographical variations. A new approximation is then proposed by adding correcting terms linked to the bathymetry. In the last part, all the previous models are integrated and compared numerically on two classical examples of bathymetry. Finally, we present a numerical study of the Green-Naghdi equations, whose range of validity is wider, and this model is compared numerically to the previous ones on specific bathymetries.
Document type :
Theses
Mathematics [math]. Université Sciences et Technologies - Bordeaux I, 2007. French


https://tel.archives-ouvertes.fr/tel-00200419
Contributor : Florent Chazel <>
Submitted on : Friday, December 21, 2007 - 3:22:07 PM
Last modification on : Wednesday, March 25, 2009 - 4:46:40 PM

Identifiers

  • HAL Id : tel-00200419, version 2

Collections

Citation

Florent Chazel. Influence de la topographie sur les ondes de surface. Mathematics [math]. Université Sciences et Technologies - Bordeaux I, 2007. French. <tel-00200419v2>

Export

Share

Metrics

Consultation de
la notice

115

Téléchargement du document

125